What is known as = a thing or personality trait she exhibits.
Who is known as = what people refer to her as.
addlehead = muddled forgetful confused incapable of serious thought.
"Susan is what is known as an addle-head" = you are describing what is wrong with Susan what she is like, her problem, what to expect when you meet her.
"Susan who is known as addle head" = Susan is called addlehead by friends.
It can be 'who is known as addlehead' if that is what people call her.